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  • Letter
  • Open Access

Quantifying measurement-induced quantum-to-classical crossover using an open-system entanglement measure

Christian Carisch1, Alessandro Romito2, and Oded Zilberberg3

  • 1Institute for Theoretical Physics, ETH Zürich, CH-8093 Zürich, Switzerland
  • 2Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
  • 3Department of Physics, University of Konstanz, 78464 Konstanz, Germany

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Phys. Rev. Research 5, L042031 – Published 29 November, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L042031

Abstract

The evolution of a quantum system subject to measurements can be described by stochastic quantum trajectories of pure states. Instead, the ensemble average over trajectories is a mixed state evolving via a master equation. Both descriptions lead to the same expectation values for linear observables. Recently, there is growing interest in the average entanglement appearing during quantum trajectories. The entanglement is a nonlinear observable that is sensitive to so-called measurement-induced phase transitions, namely transitions from a system-size dependent phase to a quantum Zeno phase with area-law entanglement. Intriguingly, the mixed steady-state description of these systems is insensitive to this phase transition. Together with the difficulty of quantifying the mixed state entanglement, this favors quantum trajectories for the description of the quantum measurement process. Here, we study the entanglement of a single particle under continuous measurements (using the newly developed configuration coherence) in both the mixed state and the quantum trajectories descriptions. In both descriptions, we find that the entanglement at intermediate time scales shows the same qualitative behavior as a function of the measurement strength. The entanglement engenders a notion of coherence length, whose dependence on the measurement strength is explained by a cascade of underdamped-to-overdamped transitions. This demonstrates that measurement-induced entanglement dynamics can be captured by mixed states.

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Phys. Rev. Research 5, L042031– Published 29 November, 2023
  • Received 6 April 2023
  • Accepted 11 October 2023
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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